While many young Americans can launch start-ups with a strategic collection of resources, would-be entrepreneurs in Cuba face many hurdles launching ventures. In the communist nation, mentorship opportunities—and even basic necessities such as consistent broadband connections—can be scarce.

A new initiative wants to change this by giving young Cuban interns a chance to learn about American entrepreneurship on U.S. soil. The unique program follows President Barack Obama's sweeping reforms in January that restored diplomatic relations with the country after 54 years.

Nearly a week ago, four young Cubans arrived in New York to begin their internship at the Grand Central Tech accelerator, which hosts start-ups for a year as they grow and scale.

"Entrepreneurs that start their own companies expect to own the fruits of their labor, but that's not currently the case in Cuba," said Miles Spencer, a tech entrepreneur and angel. "However, everything related to entrepreneurship—from problem solving to innovation and helping people—Cubans are great at," said Spencer, who founded the Greenwich, Connecticut-based nonprofit C.A.A. that runs the "Innovadores" internship.

Through mid-August, the four interns will work alongside American start-ups to learn about entrepreneurship within the areas of science, technology, engineering and math, also known as STEM fields.

The interns will take their skills back to Cuba, and hope to create a similar circle of like-minded innovators in their home country. The interns are soaking in everything New York's tech scene has to offer, including basics such as how to run a business and craft business models.

Unlimited access to U.S. technology including broadband connections are also big draws for the interns.

"You have all the right equipment here, where there is less in Havana," said Raul Perera, 20, who is studying telecommunications at the Instituto Superior Politécnico José. " I would love to see all and learn and try to pass that on to people in Havana and Cuba."

The accelerator's origins date back several months ago when Spencer attended a speech by John Caulfield, retired chief of the U.S. interests section in Havana. Caulfield described the challenges to entrepreneurship growth in Cuba.

While in Cuba, "I saw so much talent go into the arts, music and painting because that's where you could make hard currency and travel abroad," Caulfield said in an interview with CNBC.

Perera and other interns are learning the ropes from a variety of New York-based start-ups. "I hope they take back the culture and spirit of an early-stage start-up—that it's really hard but that it is possible," said Kate Ryder, founder and chief executive of Maven, which offers on-demand video appointments with health and wellness providers to women.

Ryder is working with Gabriela Rodriguez, a physics student at Havana University. Rodriguez sees the accelerator as a building block for her trajectory into launching her own start-up one day.

"I should be ready for it," said Rodriguez, 18 "There's a lot of potential in Cuba, a lot of smart people who work really hard, but there's maybe not so much opportunity. We would like to give back and at least help them to have that."